Question

3. The amplitude of oscillation of a mass attached to a spring decreases by 10% with each oscillation. By what percent does the energy of the system decrease with each oscillation? Potential Energy of a mass - spring system is; E = ½ kx2 . Here k is the force constant of the spring and x is the displacement.

4. A small child weighing 200N sits on a swing of length 2.2 m.

(a) Find the period for small- amplitude oscillations, treating the swing as a simple pendulum.

(b) Suppose that the child swing system gradually slows down in such a way that on each successive swing the maximum y - coordinate of the child’s center of gravity is 3.00 mm less than on the precious swing.

(i) How much energy would have to be supplied by a parent pushing the child to maintain a constant amplitude.

(ii) At what rate should this energy be supplied?

Answer 1

In question number 4, I am taking value of g=10 .If you find some variation in answer then take g = 9.81